Home
Class 12
MATHS
(i) Check the validity of given statemen...

(i) Check the validity of given statement
r : A triangle is iosceles if and only if its two angles are equal
(ii) Using the word " necessary and sufficent " rewrite the statement " A sequnece is in G. P if and only if each term differs from the succeeding one by a non-zero constant ratio

Text Solution

Verified by Experts

(i) Component statements are
p : A tringle is isosceles
q : Two angles of a triangle are equal
To check the validity of r, first we asseme that p is true , i.e.,triangle is isosceles then its sides are equal , so it's two angles are also equal . Hence , q is true
Now, assuming that q is true , that two angles of a triangle are equal then their corresponding two sides are also equal so triangle is isosceles . Hence , p is also true
Statement r is valid
(ii) The necessary and sufficent condition for a sequence is in G.P is that each term must be differs from the succeeding one by a non-zero constant ratio
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-A) (Objective type Questions (Only one answer))|50 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-B) (Objective type Questions (Only one answer))|10 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE|Exercise Assignment (SECTION-D) (Assertion-Reason Type Questions)|15 Videos
  • LIMITS AND DERIVATIVES

    AAKASH INSTITUTE|Exercise Section - j|3 Videos
  • MATRICES

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|3 Videos

Similar Questions

Explore conceptually related problems

Using the word " necessary and sufficent" rewrite the statement "j sqrtn is a rational number if and only if is a pefect square

Using the words necessary and sufficient rewrite the statement The integer n is odd if and only if n^(2) is odd Also check whether the statement is true.

Using the words 'necessary and sufficient rewrite the statement The integer n is odd if and only if n^(2) is odd .Also check whether the statement is true.

Rewrite each of the following statements in the form p if only if q:r: For you to get an A grade,it is necessary and sufficient that you do all the homework you regularly.

Check the validity of given statement (a) r : 31 is odd and prime number (b) r : Range of f(x)=x^2 " is " R^+ U {0} and it is even function (ii) From compound statement with given statement by using connective "and" and check its "validity" p : Bhopal is in U.P q : Bhopal is the captial of M.P

Check the validity of the following statement (a) p : 77 is a multiple of 11 or 7 (b) q : If an integer x is multiple of 20 , then it is multiple of 10 (c ) For the given statement, identify the necessary and sufficient condition r : If numerator of a ratio is smaller than denomenator then the ratio is in proper fraction

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are suflicient to answer the question. Read, both the statements and give answer 1) if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question. 2) if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question. 3) if the data either in- statement I alone or in statement II alone 'are sufficient to answer the question. 4) if the data even in both statements I and II together are not sufficient to answer the question. 5) if the data in both statements I and II together are necessary to answer the question. How is M related to D? I. D says I have only one brother. II. M says I have only one sister.

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are suflicient to answer the question. Read, both the statements and give answer 1) if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question. 2) if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question. 3) if the data either in- statement I alone or in statement II alone 'are sufficient to answer the question. 4) if the data even in both statements I and II together are not sufficient to answer the question. 5) if the data in both statements I and II together are necessary to answer the question. How is Nandini related to Santosh ? I. Nandini’s brother is the only grandson of Santosh’s father. II. Nandini has only one brother.

Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are suflicient to answer the question. Read, both the statements and give answer 1) if the data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question. 2) if the data in statement II alone are sufficient to answer the question while the data in statement I alone are not sufficient to answer the question. 3) if the data either in- statement I alone or in statement II alone 'are sufficient to answer the question. 4) if the data even in both statements I and II together are not sufficient to answer the question. 5) if the data in both statements I and II together are necessary to answer the question. How is P related to Q? I. J has two daughters, one of them 'R’ is married to 'P’ II. Q is the mother of 'S’, the younger sister of ‘R’

AAKASH INSTITUTE-MATHEMATICAL REASONING-Try Yourself
  1. Which of the following sentences are statement ? (i) Cow is the onl...

    Text Solution

    |

  2. Check whether the following sentences are statement or not also provid...

    Text Solution

    |

  3. Write the negation of the following statements (i) sqrt(13) is ratio...

    Text Solution

    |

  4. Write the negation of the following statements and check whether the r...

    Text Solution

    |

  5. Find the component statement of the following compound statement , Che...

    Text Solution

    |

  6. Write the component statement of the following statement and check whe...

    Text Solution

    |

  7. For each of the following statement , determine whether an inclusive "...

    Text Solution

    |

  8. Identify the type of OR used in following statement and check whether ...

    Text Solution

    |

  9. Identify the quantifier in the following statement and write the negat...

    Text Solution

    |

  10. Rewrite the following statement with "if then" in five different ways...

    Text Solution

    |

  11. Write contrapositive of the following statement (i) If an Indian is ...

    Text Solution

    |

  12. Write the converse of the following statement (a) If H. C. F. of (a,...

    Text Solution

    |

  13. Given below are two pairs of statement , combine these two statement u...

    Text Solution

    |

  14. Check the validity of given statement (a) r : 31 is odd and prime nu...

    Text Solution

    |

  15. Check the validity of the following statement (a) p : 77 is a multip...

    Text Solution

    |

  16. (i) Check the validity of given statement r : A triangle is iosceles...

    Text Solution

    |

  17. (i) Verify by method of contradicition p : There are infinitely many...

    Text Solution

    |

  18. By giving counter example show that following statement are false (a...

    Text Solution

    |